In the past, power output from a device such as a gravity meter had to be measured over a long term TA, in order to determine long term stability of the power output from the device. Variations, Delta PT2, Delta PT3 . . . Delta PTA from a null power output value, P, of the device would be measured over the term TA. This period of time TA would be needed to determine a long term variation Delta PTA from the null power output value P. TA is an empirically determined drift cycle time for power output variations of such devices.
The present method allows one to determine Delta PTA, as an indication of long term stability of power output, without having to take measurements of power output over a long term TA. The present method allows one to determine long term stability of power output of the device, even though measurements are not taken over a period of a drift cycle time, TA.
In the present method, measurements of the power output values PT2, PT3 etc. of the gravity meter are made at intervals of time T2, T3, T4 etc, until a length of time T1 is reached. Here T3 equals twice T2. T4 equals three times T2. A power output plot versus time, is formed from the set of power output values.
A center line is drawn through the power output plot. This center line represents the constant power output,P, of the gravity meter. A set of power output variation values, Delta PT2, Delta PT3 . . . Delta PT1 from value P is calculated. The vavalues in this set is correspond to the regular intervals of time from T2 to T1.
A Fourier transform of each power output variation, Delta PT2, Delta PT3, . . . Delta PT1, is made. A power spectral density value PSD is calculated. PSD is the value of the Fourier transform at a particula frequency fT, where fT equals 1/T. For example, a power spectral density value, (PSD)T2, is the value of the Fourier transform of Delta PT2, at the frequency f2=1/T2. A power spectral density value (PSD)T3 is the value of the Fourier transform of Delta PT3 at the frequency f3=1/T3. A power spectral density value (PSD)T1 is the value of the Fourier transform of Delta PT1 at the frequency f1=1/T1.
The log of each calculated power spectral density value is ploted against the log of a frequency associated with the length of time required to find a power output variation associate with each calculated power spectral density value. The plotting is done on log-log paper. This log-log paper is an example of a log-log form.
The power spectral density log plot can be extrapolated, in order to find a log of a power spectral density value (PSD)TA a a value that is the log of a frequency fA=1/TA. The value of (PSD)TA and fA are found from the log values of (PSD)TA and fA.
The inverse Fourier transform of the power spectral density value (PSD)TA is taken in order to find the variation, Delta PTA.
One can determine a line of slope of the power spectral density plot, and can therefore extrapolate the line of slop. plot. This determination of a lione of slope is performed by examining the power spectral densty plot generated from data taken over a length of time T1, that is at intervals T2, T3, T4 . . . T1.
One does not have to measure a power variation, Delta PTA, in the power output of a gravity meter at a time TA, in order to determine the power output drift, or variation, for this time TA. One can merely measure the slope of the power spectral density curve in order to predict the value of the power spectral density at a time, TA, and take the inverse Fourier transform of that value.
Further one can find noise power, PTATB, in a bandwith between fA and fB, where fB is smaller than f2. One first integrates a power density function, S(f), that gives the ploted power spectral density, (PSD)T, between f1 and f2, to find a noise power PT1T2. Then one uses the value PT1T2 in an algorithm to find PTATB.